Subgroups — #13113501

Order 1664.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	#11718586	C₂	1	2	yes	maximal
3	#11718139	C₂	1	4	yes	maximal, complemented
4	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
5	C₁₃×#125	C₄	1	2	yes	—
6	C₁₃×C₂²⋊Q₈	—	2	2	no	—
7	C₄×Q₈×C₁₃	—	2	2	no	—
8	C₁₃×#117	C₄	1	2	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²⋊#1055	—	2	2	no	—
11	C₄⋊#1055	C₂²	1	4	yes	—
12	C₄×#1055	—	2	2	no	—
13	C₂×Q₈×C₁₃	—	2	2	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	D₄	1	2	yes	—
16	C₁₃×C₄⋊C₄	—	2	4	no	—
17	C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
19	C₁₃×C₂²⋊C₄	—	2	2	no	—
20	C₄²×C₁₃	—	2	2	no	—
21	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₃	D₄	1	2	yes	—
23	C₄²×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×#1055	—	2	4	no	—
25	#1544	—	13	1	no	maximal, Sylow
26	C₂³×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	Q₈×C₁₃	—	4	4	no	—
28	C₂×C₄×C₁₃	—	2	2	no	—
29	C₂×C₄×C₁₃	—	2	4	no	—
30	C₂×C₄×C₁₃	—	2	4	no	—
31	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
35	#1055	—	4	4	no	—
36	#533	D₁₃	1	1	yes	characteristic
37	#431	—	13	2	no	—
38	#332	—	13	4	no	—
39	C₂²×C₁₃	—	2	1	no	—
40	C₂²×C₁₃	—	2	2	no	—
41	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	—	2	2	no	—
44	C₄×C₁₃	—	4	4	no	—
45	C₄×C₁₃	#101	1	2	yes	—
46	C₄×C₁₃	#135	1	4	yes	—
47	C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
48	#125	Dic₁₃	1	2	yes	—
49	C₂²⋊Q₈	—	2	2	no	—
50	C₄×Q₈	—	2	2	no	—
51	#117	Dic₁₃	1	2	yes	—
52	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
53	C₄⋊C₈	—	13	4	no	—
54	C₂²⋊C₈	—	26	2	no	—
55	C₄×C₈	—	26	2	no	—
56	C₂×C₁₃	—	4	1	no	—
57	C₂×C₁₃	C₂×#101	1	1	yes	characteristic
58	C₂×C₁₃	#416	1	2	yes	—
59	C₂×Q₈	—	2	2	no	—
60	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
61	C₂²×C₄	C₂²⋊D₁₃	1	2	yes	—
62	C₂×C₈	—	26	4	no	—
63	C₄⋊C₄	—	2	4	no	—
64	C₄⋊C₄	—	2	2	no	—
65	C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
66	C₂²⋊C₄	—	2	2	no	—
67	C₄²	—	2	2	no	—
68	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
69	C₄²	C₂²⋊D₁₃	1	2	yes	—
70	C₄²	C₂²×D₁₃	1	1	yes	characteristic
71	C₁₃	#1544	1	1	yes	characteristic, complemented, Sylow
72	C₂³	C₂²⋊Dic₁₃	1	1	yes	characteristic
73	Q₈	—	4	4	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	C₂²⋊Dic₁₃	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
79	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
80	C₂×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
81	C₈	—	52	4	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	2	2	no	—
87	C₄	—	4	4	no	—
88	C₄	#88076	1	2	yes	—
89	C₄	#88204	1	4	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₂×#88076	1	1	yes	characteristic
92	C₂	#11718894	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#533	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₃	C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂³
hypercenter	#533	D₁₃
hypocenter	C₁₃	#1544
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #11718139	C₂	semidirect
71. C₁₃	#1544	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#533	2
#11718586	2
#11718139	2
#1544	13